I believe a coil spring trap is where the animal steps in the center and it catches the leg. The traps we use are "humane" traps, where you put the bait on one end, and the animal crawls inside the cage and steps on the trigger before it gets to the food, which springs the door shut.
Coil springs are generally regarded as better, because you are not fully relying on the animal to be dumb enough to crawl inside a small space. However, if you have other animals around that might get their leg caught, the coil spring is probably not for you. (We've got a dog and barn cats, so coil springs won't work for us.)